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![[y] denotes the greatest integer less than or equal to y. Is d < 1?](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "[y] denotes the greatest integer less than or equal to y. Is d < 1?"){kind=icon}
20 Feb 2014, 01:14
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D
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[y] denotes the greatest integer less than or equal to y. Is d < 1?
(1) d = y - [y]
(2) [d]= 0
(1) d = y - [y]
(2) [d]= 0
20 Feb 2014, 01:14
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SOLUTION
[y] denotes the greatest integer less than or equal to y. Is d < 1?
Some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...
Question: is \(d<1\)?
(1) d = y - [y] --> if y is an integer then \([y]=y\) and \(d=y-[y]=0<1\), if y is not an integer [y] is nearest integer less than y and still \(d=y-[y]<1\) (for example: \(y=1.5\) --> \(d=1.5-[1.5]=1.5-1=0.5<1\) or \(y=-1.5\) --> \(d=-1.5-[-1.5]=-1.5-(-2)=0.5<1\) ). Sufficient.
(2) [d] = 0 --> \(0\leq{d}<1\). Sufficient.
Answer: D.
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Hope it helps.
[y] denotes the greatest integer less than or equal to y. Is d < 1?
Some function [] rounds DOWN a number to the nearest integer. For example [1.5]=1, [2]=2, [-1.5]=-2, ...
Question: is \(d<1\)?
(1) d = y - [y] --> if y is an integer then \([y]=y\) and \(d=y-[y]=0<1\), if y is not an integer [y] is nearest integer less than y and still \(d=y-[y]<1\) (for example: \(y=1.5\) --> \(d=1.5-[1.5]=1.5-1=0.5<1\) or \(y=-1.5\) --> \(d=-1.5-[-1.5]=-1.5-(-2)=0.5<1\) ). Sufficient.
(2) [d] = 0 --> \(0\leq{d}<1\). Sufficient.
Answer: D.
Similar questions to practice:
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if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html
is-x-an-odd-integer-1-x-2-2x-99856.html
for-all-z-denotes-the-least-integer-greater-than-or-110561.html
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awkward-ds-105416.html
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if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html
denotes-to-be-the-least-integer-no-less-than-x-is-130841.html
is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html
if-denotes-the-greatest-integer-less-than-or-equal-to-z-162078.html
if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html
is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html
for-all-z-denotes-the-least-integer-greater-than-or-equ-167640.html
Hope it helps.
Updated on: 22 Mar 2022, 10:43
Originally posted by BrentGMATPrepNow on 19 Apr 2018, 13:34.
Last edited by BrentGMATPrepNow on 22 Mar 2022, 10:43, edited 1 time in total.
Last edited by BrentGMATPrepNow on 22 Mar 2022, 10:43, edited 1 time in total.
Kudos
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Bunuel
First, let's take a moment to get a good idea of what this strange notation means.
A few examples:
[5.1] = 5
[3] = 3
[8.9] = 8
[-1.4] = -2
[-13.6] = -14
IMPORTANT FACT #1: [y] < y
IMPORTANT FACT #2: The difference between y and [y] is always less than 1. In other words, y - [y] < 1
Target question: Is d < 1?
Statement 1: d = y - [y]
Take IMPORTANT FACT #1 from above: [y] < y
Subtract [y] from both sides to get: 0 < y - [y]
Now take IMPORTANT FACT #2 and add it to our inequality to get: 0 < y - [y] < 1
Statement 1 tells us that d = y - [y], so let's replace y - [y] with d to get: 0 < d < 1
PERFECT, we can now be certain that d < 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: [d] = 0
We're going to use IMPORTANT FACT #2 in our solution.
Take [d] = 0 and add d to both sides to get: [d] + d = d
Subtract [d] from both sides to get: d = d - [d]
From IMPORTANT FACT #2, we know that d - [d] < 1
Since we just showed that d = d - [d], we can be certain that d < 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
